Information Scrambling versus Decoherence—Two Competing Sinks for Entropy

Abstract

A possible solution of the information paradox can be sought in quantum information scrambling. In this paradigm, it is postulated that all information entering a black hole is rapidly and chaotically distributed across the event horizon, making it impossible to reconstruct the information by means of any local measurement. However, in this scenario, the effects of decoherence are typically ignored, which may render information scrambling moot in cosmological settings. In this work, we develop key steps toward a thermodynamic description of information scrambling in open quantum systems. In particular, we separate the entropy change into contributions arising from scrambling and decoherence, for which we derive statements of the second law. This is complemented with a numerical study of the SachdevYe-Kitaev, Maldacena-Qi, XXX, mixed-field Ising, and Lipkin-Meshkov-Glick models in the presence of decoherence in the energy or in the computational basis.